Simple Machine Simple Machines • Changes effort, displacement or direction and magnitude of a load • 6 simple machines – Lever – Incline plane – Wedge – Screw – Pulley – Wheel and Axle • Mechanical Advantage 퐸푓푓표푟푡 퐷푠푡푎푛푐푒 퐿표푎푑 퐿 – Ideal: IMA = = = Note: (Effort Distance•Effort) =(Load Distance•Load) or Ein=Eout 퐿표푎푑 퐷푠푡푎푛푐푒 퐼푑푒푎푙 퐸푓푓표푟푡 퐸퐼 퐿표푎푑 퐿 – Actual: AMA= = 퐴푐푡푢푎푙 퐸푓푓표푟푡 퐸퐴 • Efficiency how the effort is used to move the load – Losses due to friction or other irreversible actions 퐸푛푒푟푔푦 푢푠푒푑 퐴푀퐴 퐸퐼 – η= = = Note: (EA=EI-Loss) 퐸푛푒푟푔푦 푠푢푝푝푙푒푑 퐼푀퐴 퐸퐴 2/25/2016 MCVTS CMET 2 Lever • Levers magnify effort or displacement • Three classes of levers based on location of the fulcrum 150lb – Class 1 lever: Fulcrum between the Load and Effort Examples: See-Saw, Pry Bar, Balance Scale – Class 2 lever: Load between the Effort and Fulcrum Examples: Wheelbarrow, Nut Cracker – Class 3 Lever: Effort between Load and Fulcrum Examples: Elbow, Tweezers Effort η=0.9 푑퐸 퐿 • 퐼푀퐴퐿푒푣푒푟 = = 푑퐿 퐸퐼 퐿 푑 8 • 퐴푀퐴 = 푒 퐿푒푣푒푟 퐸 퐼푀퐴 = = = 2 퐴 푑퐿 4 퐴푀퐴퐿푒푣푒푟 퐸퐴 퐿 150 • η= = 퐸 = = = 75푙푏 퐼푀퐴퐿푒푣푒푟 퐸퐼 퐼 퐼푀퐴 2 퐴푀퐴 = η퐼푀퐴 = 0.9 ∙ 2 = 1.8 퐿 150 퐸 = = = 83.33푙푏 퐴 퐴푀퐴 1.8 2/25/2016 MCVTS CMET 3 Incline Plane • Decreases effort to move a load to a new height or vertical rise Vert. • Friction opposes motion up the ramp increasing Rise the effort required (h) 푠 1 • 퐼푀퐴 = = ℎ 푠푛휃 θ 퐸푛푒푟푔푦 푢푠푒푑 퐴푀퐴 퐸 • η= = = 퐼 퐸푛푒푟푔푦 푠푢푝푝푙푒푑 퐼푀퐴 퐸퐴 θ w Ex. An incline plane with 20°slope is used to move a ℎ 36 a) 푠 = = = 105.3 푖푛 50-lb load a vertical distance of 36 inches. The actual 푠푛휃 푠푛20° amount of effort force that is needed to move the 푠 105.3 b) 퐼푀퐴 = = = 2.92 load up the inclined surface is 25lb. Find: ℎ 36 퐿 50 a) Travel distance c) 퐴푀퐴 = = = 2 b) Ideal mechanical advantage 퐸퐴 25 퐴푀퐴 2 c) Actual mechanical advantage d) η = = = 0.68 퐼푀퐴 2.92 d) Efficiency, η 퐿 50 e) 퐸 = = = 17.12 푙푏 e) Ideal effort 퐼 퐴푀퐴 2.92 2/25/2016 MCVTS CMET 4 Wedge • Wedge is similar to incline ramp but different things move – Incline Plane o Incline plane is stationary o Only one surface is involved – Wedge o Wedge moves and load is stationary o Friction forces on both sides of the wedge • Wedge benefits – Redirects force from horizontal to vertical or vice versa – Uses friction forces to create self-locking designs – Usese: Splitting wood, Door stops, Shimming to level items, raise or lower objects, etc. • Wedge – Force P moves wedge if it overcomes friction forces – Sliding occurs on three surfaces and subjected to friction forces – Two conditions with applied force o Does it overcome the friction force? o Does the downward force of the weight, W, overcome the friction force and the applied force, P, if any, so that the wedge pops out. 2/25/2016 MCVTS CMET 5 Wedge Free Body • Friction force opposes motion • Applied force to the right controls movement of the weight • Wedge weight is considered negligible as compared to the load weigh Lowering Weight – Lowering weight – Raising Weight Non Self-locking Self-Locking 2/25/2016 MCVTS CMET 6 Friction force - Revisited • Friction force opposes motion • Friction force is proportional to the normal force – Ff=μsFN where μs is the coefficient of static friction and FN is the normal force – Friction force, Ff can also be expressed as a “Friction Angle, ψ” 퐹 푓 2 2 o tan ψ = , where 푅 = 퐹푁 + 퐹푓 퐹푁 F ψ F FN 2/25/2016 MCVTS CMET 7 Example Block A supports a load W=100kN and is to be raised by forcing the wedge B under it. The angle of friction for all services in contact is f=15°. If the wedge has a weight of 40kN, find the value of P : a) To start the wedge under the block b) To pull the wedge out from under the block 2/25/2016 MCVTS CMET 8 Solution 2/25/2016 MCVTS CMET 9 Problem Part 2 2/25/2016 MCVTS CMET 10 2/25/2016 MCVTS CMET 11 Wheel and Axle New • Uses the mechanical advantage to either magnify the applied force or magnify the motion d1 d2 • Raising Bucket: – Load is inner shaft – Effort on large wheel • Driving Car: – Load is tire F2 F1 – Effort is drive Axle 퐿표푎푑 퐸푓푓표푟푡 퐷푠푡. 2휋(푟2) 푟2 Mechanical Advantage: 푴푨퐼푑푒푎푙 = = = = 퐸푓푓표푟푡 퐿표푎푑 퐷푠푡. 2휋(푟1) 푟1 푴푨 Efficiency: η= 푎푐푡푢푎푙 푴푨푖푑푒푎푙 Basic Screw Terminology New Pitch – Distance between adjacent threads Lead – Distance screw (or nut) advances per full turn Lead=Pitch*Starts (for single thread start=1) Start – Number of separate (non-intersecting) threads wound around the same core Maj. Diam. – Diameter over the top of the thread Min. Diam. – Diameter at the root of the thread Pitch Diam. – Diameter through the thread at the point where the thread thickness is equal to ½ the pitch Standard Thread Designation UNC and UNF SI Thread XXX-YYY Maaa-bbb XXX – Major diameter aaa – Major diameter (mm) For Ø>¼” actual diameter bbb – Pitch (mm/thread) For Ø<¼” Gauge number (4, 6, 8, 10 or 12) YYY- Threads/inch 퐿표푎푑 퐸푓푓표푟푡 퐷푠푡. 2휋(푟 Mechanical Advantage: 푴푨 = = = 푒푓푓표푟푡) 퐼푑푒푎푙 퐸푓푓표푟푡 퐿표푎푑 퐷푠푡. 푙푒푎푑 푴푨 Efficiency: η= 푎푐푡푢푎푙 푴푨푖푑푒푎푙 Power Screws New • Power Screws – Used to transmit power or motion – Axial movement of nut supplies motion • Screw Profiles – Square Thread o Most efficient for transferring torque to linear motion – Acme Thread o Easeier to make o Good when well lubricated o Efficeincy slightly lower than Squrare thread – Butress Thread o More efficient than Acme o Closer to square thread o Used when force is transmitted in one direction only.